A new record for arrivals at Heathrow is expected to be set on Thursday, with up to 125,000 incoming passengers

On Wednesday night, Games organisers apologised to North Korean athletes whose images were shown next to the South Korean flag.

Mr Cameron earlier played down the flag blunder, which happened on the first day of sporting action, and delayed the women's football match between North Korea and Colombia at Glasgow's Hampden Park by about an hour.

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Media captionOrganisers have released a short clip from the dress rehearsal of the Olympic Games opening ceremony

"This was an honest mistake, honestly made," Mr Cameron said.

"An apology has been made and I'm sure every step will be taken to make sure these things don't happen again."

The prime minister called the eve of the Games "a truly momentous day for our country".

"Seven years of waiting, planning, building, dreaming, are almost over - tomorrow, the curtain comes up, the spectators arrive, and the Olympic and Paralympic Games 2012 can officially begin."

Mr Cameron earlier met the Republican candidate for the US presidency, Mitt Romney, during his campaigning and fundraising visit to London.

The meeting came after Mr Romney expressed concerns about "disconcerting" signs of a lack of readiness for the Games.

"The stories about the private security firm not having enough people, the supposed strike of the immigration and customs officials - that obviously is not something which is encouraging," Mr Romney told a US television station.

It was "hard to know just how well it will turn out", said Mr Romney, who managed the Winter Olympics in Salt Lake City in 2002.

Mr Cameron responded: "Of course, this is a time of some economic difficulty for the UK. Everybody knows that.

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Media captionMitt Romney: "I'm excited about the opening of the Olympics"

"But look at what we're capable of achieving as a nation, even at a difficult economic time."

He added: "In terms of the country coming together, I think the torch relay really demonstrates that this is not a London Games, this is not an England Games, this is a United Kingdom Games.

"I think we'll show the whole world not just that we've come together as a united kingdom, but also we're extremely good at welcoming people from across the world."

Mr Romney, who also met Labour leader Ed Miliband, later said outside Number 10: "I expect the Games to be highly successful."